Prepositioning Network Design for Humanitarian Relief Purposes under Spatially Correlated Demand Uncertainty

Prepositioning relief network is an effective strategy to mitigate the impact of natural disasters and public health emergencies, such as the ongoing COVID-19 pandemic. However, designing a proper network is challenging due to limited information and, more importantly, the spatially correlated demand uncertainty that exists among affected areas. We consider a network design problem for humanitarian relief purposes, where spatial demand correlations exist and demand information is limited, i.e., only the mean demand and covariance matrix are known. Note that the covariance matrix can explicitly capture the spatially correlated demand among areas. We formulate this problem as a mixed-integer two-stage distributionally robust location-inventory model, which is generally NP-hard and computationally intractable. The model is further reformulated as a mixed-integer conic problem based on copositive cones, and it is tractable with positive semidefinite relaxation. To accelerate the problem-solving process, we design an interpretable branching-and-pricing heuristic with a warm start. Both case study and simulation results demonstrate that explicitly modeling spatial demand correlation can decrease unmet demand